Inference for volatility-type objects and implications for hedging
Mykland, P.A. and Zhang, L.
The paper studies inference for volatility type objects and its
implications for the hedging of options. It considers the nonparametric
estimation of volatilities and instantaneous covariations between
diffusion type processes. This is then linked to options trading, where we
show that our estimates can be used to trade options without reference to
the specific model. The new options ``delta'' becomes an additive
modification of the (implied volatility) Black-Scholes delta. The
modification, in our example, is both substantial and statistically
significant. In the inference problem, explicit expressions are found for
asymptotic error distributions, and it is explained why one does not in
this case encounter a bias-variance tradeoff, but rather a
variance-variance tradeoff. Observation times can be irregular.
Keywords: volatility estimation, statistical uncertainty, small
interval asymptotics, mixing convergence, option hedging